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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 95370db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.dc4 | 95370db1 | \([1, 0, 0, -2112596, 1181700240]\) | \(43199583152847841/89760000\) | \(2166588193440000\) | \([2]\) | \(1769472\) | \(2.1921\) | \(\Gamma_0(N)\)-optimal |
95370.dc3 | 95370db2 | \([1, 0, 0, -2135716, 1154506496]\) | \(44633474953947361/1967006250000\) | \(47478749082806250000\) | \([2, 2]\) | \(3538944\) | \(2.5386\) | |
95370.dc5 | 95370db3 | \([1, 0, 0, 1106864, 4351041860]\) | \(6213165856218719/342407226562500\) | \(-8264878057250976562500\) | \([2]\) | \(7077888\) | \(2.8852\) | |
95370.dc2 | 95370db4 | \([1, 0, 0, -5748216, -3782336004]\) | \(870220733067747361/247623269602500\) | \(5977023756035946322500\) | \([2, 2]\) | \(7077888\) | \(2.8852\) | |
95370.dc6 | 95370db5 | \([1, 0, 0, 15132034, -24942381354]\) | \(15875306080318016639/20322604533582450\) | \(-490538269189059204064050\) | \([2]\) | \(14155776\) | \(3.2318\) | |
95370.dc1 | 95370db6 | \([1, 0, 0, -84428466, -298565760654]\) | \(2757381641970898311361/379829992662450\) | \(9168172656159380584050\) | \([2]\) | \(14155776\) | \(3.2318\) |
Rank
sage: E.rank()
The elliptic curves in class 95370db have rank \(0\).
Complex multiplication
The elliptic curves in class 95370db do not have complex multiplication.Modular form 95370.2.a.db
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.